Surprisingly, this is incorrect! We need a King to make a better connection with Hashem. The "Moses of the Generation" holds this very special role as leader of the Jewish people.
God could just as well have taken the Jews out of Egypt WITHOUT a Moses! He could have done all those miracles, and then some, to make the Egyptians chase the Jews from their presence, but, in fact, that's not the way Hashem proceeded. He wanted a "Moses" for every generation.
That's the way Hashem designed the Jewish collective body. IT NEEDS A HEAD, as sure as the individual himself needs a head. And that head exists whether the Jew knows it or not!
Hashem provides the Jewish nation with a "conduit" to reach Him. Without that conduit, the spiritual component of the bond between Hashem and His people could not sustain itself otherwise. Something in the connection will snap if that conduit were absent. The Jewish king or leader in every generation, as Moshe said (Devarim 5:5), stands between Hashem and the Jew to establish an unmitigated bond:
For that bond to Hashem to be intimate, so we do what He wants of us, as in doing His commandments, we need superb motivation and, most importantly, we need plenty of humility to accept God's yoke upon us. The King makes that self-nullification process in the Jew easier to render. The "Moses of the Generation", as a mediator between the Jew and God, is a very special "conduit".
All conduits, by their nature, automatically impose an element of "self" that compromises the channel, even if slightly. In Chassidut, this concept they call "a compromising conduit". A physical analogy could be the "friction" the conduit places on fluid that passes through the conduit to get from one compartment to the next. However slight the friction by this intermediary pipe, it still offers resistance to the flow.
Thus ALL conduits inflict some measure of "interference" when mediating between parties because the mediator has his own personality that cannot become irrelevant; To behave as if he were physically absent is an impossibility and therefore the mediation is less than 100% perfect.
The Moses of the generation is the sole mediator who can mediate with complete self-nullification, without getting his own interests to conflict whatsoever with the needs of the Jew. Only the Moses of the generation is the perfect, frictionless conduit to secure the unbreakable bond between Jew and Hashem.